We investigate a family of regression problems in a semisupervised setting. The task is to
assign real-valued labels to a set of n sample points provided a small training subset of N …

This paper establishes the consistency of spectral approaches to data clustering. We
consider clustering of point clouds obtained as samples of a ground-truth measure. A graph …

Existing generalization analysis of clustering mainly focuses on specific instantiations, such
as (kernel) $ k $-means, and a unified framework for studying clustering performance is still …

This paper establishes the consistency of a family of graph-cut-based algorithms for
clustering of data clouds. We consider point clouds obtained as samples of a ground-truth …

In this paper, we propose a new covering technique localized for the trajectories of SGD.
This localization provides an algorithm-specific complexity measured by the covering …

Scalings in which the graph Laplacian approaches a differential operator in the large graph
limit are used to develop understanding of a number of algorithms for semi-supervised …

In this paper we develop a numerical method for solving a class of optimization problems
known as optimal location or quantization problems. The target energy can be written either …

Fatou's lemma is a classic fact in real analysis stating that the limit inferior of integrals of
functions is greater than or equal to the integral of the inferior limit. This paper introduces a …

This paper describes Fatou's lemma for a sequence of measures converging weakly to a
finite measure and for a sequence of functions whose negative parts are uniformly …

The software-defined network (SDN) allows us to control network flows easily and
dynamically. Intrusion detection systems (IDS) are among the controller's applications. The …